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18 October 2001 Reference solution for thermal mine signature modeling
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Predicting the thermal signature of a buried land mine requires modeling the complicated inhomogeneous environment and the structurally complex mine. It is useful, both in checking such models and in making rough calculations of expected signatures, to have an accurate, easily computed solution for a relatively simple geometry. In this paper, a reference solution is presented for the integral equation that governs the temperature distribution. Our solution procedure uses the method of weighted residuals. The problem comprises a homogeneous cylindrical body (the mine model) buried in an infinite homogeneous half space (the soil model) with a planar interface. Using periodic boundary conditions in time at the planar interface, the temperature distribution in the lower-half space is expanded in a Fourier series. A volume integral equation for the Fourier series coefficients is obtained via Green's second identity. The Green's function for the Fourier coefficients is derived and reduced to a computationally efficient form. The integral equation is reduced to a matrix equation, which is then solved for the unknown temperature distribution. The integral equation solution is compared with a finite element model.
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Ibrahim Kursat Sendur and Brian A. Baertlein "Reference solution for thermal mine signature modeling", Proc. SPIE 4394, Detection and Remediation Technologies for Mines and Minelike Targets VI, (18 October 2001);

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